## The motion of the Moon

The motion of the Moon is much more complex than that of the Sun and it cannot be described by a simple eccentric circle mechanism. The reasons for this were known to Hipparchus and are stated by Ptolemy: they are that first the Moon moves with varying speed in such a way that over the course of time it achieves its maximal speed for every value of its longitude X, and, second, that

8 More details of how Hipparchus arrived at his solar model can be found in Jones (1991b), and Maeyama (1998) has analysed the effect of observational errors on the underlying parameters and hence on the predictions of the model. According to Jacobsen (1999) the maximum error in Hipparchus' theoretical values for the Sun's longitude was about 22'. A theory developed in the 1920s that credits the Babylonians with the discovery of precession was shown to be false by Neugebauer (1950).

Ptolemy Almagest, Book VII, 2. Ptolemy stated that Hipparchus wrote a work (now lost) entitled On the Displacement of the Solstitial and Equinoctial Points. Surprisingly perhaps, Hipparchus' discovery was mentioned by only a few Greek writers (see Dreyer (1953), p. 203); it took on a much greater significance in later centuries. Ptolemy Almagest, Book IV, 2.

the Moon does not move on the ecliptic, but instead has latitudes which vary between ± 5° of the ecliptic in such a way that the Moon achieves its maximal latitude for every value of X .Itisa simple matter to see that a model like that used by Hipparchus for the Sun will lead always to the maximal speed occurring for the same value of the longitude (at the perigee - the point on the orbit closest to the Earth) and so cannot account for the first of these observations. The second observation suggests that the orbit of the Moon is inclined at an angle of about 5° to the ecliptic. However, if the line joining the intersections of the Moon's orbit and the ecliptic is fixed, the maximum latitude always will occur for the same value of the longitude which is observed not to be the case. In order for an eclipse to occur, the Moon must be near one of its nodes and thus observations of eclipses can be used to give fairly accurate information on the nodes of the Moon's orbit. Lunar periods had been computed accurately by the

Babylonians, and Hipparchus, by comparing his own observations with earlier

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